Not exactly that, no. On many systems, each separate ARGB header is treated as a distinct controller output that can be controlled individually by the controller system. That detail depends on how that controller system was designed - to have individual controllers for each header, or to connect all headers in parallel to a single controller. It also depends on whether the ARGB software utility can work that way, but I would assume that, IF the controller hardware can offer multiple controllers, its software would make use of that feature. I do know that some third-party systems (not on mobos) have at least two separate RGB controller "channels" that can be configured differently using their maker's software.
Most mobos have only ONE ARGB header, so that discussion is moot. I will note also that this is all consistent with the design of ARGB light strips, including the lights in fan frames. RGB light strips contain LED's of three colours normally - Red, Green, and Blue. In an ARGB system, all of them are arranged in Nodes. Each Node contains one LED of each colour and its own Control Chip that controls those theee LED's only. Along the strip, each Control Chip has its own unique address. It listens on a common Address Line for instruction packets adressesd to that Node only and follows that. But from one light strip to another, the addresses for the individual Noe control chips are the same. That is, on virtually all ARGB light strips, the first LED Node groups have the same addresses, and the second Nodes have the same addesses as other strips, which is different from the first Nodes' address, etc. There is no provision for a separate address to be assigned to an indicidual strip. So the only way to get different ARGB strips to display different patterns is to send each strip separate data streams geneeated by separate master controllers, and fed though separate headers.
I was assuming that your mobo has ONE ARGB headeer and hence one controller, and that thus you have all of your ARGB lighting units connected to that one resource by using an ARGB Splitter. That is why all the fans etc. will display exactly the same things. If you want them different, you will have to get and install additional ARGB controllers, one for each strip / fan. BUT even then you will have a dilemma trying to use some software tools to set each separate controller to do different things.
In passing, I will note your thoughts are pretty much opposite from what many others want. So many people want to be sure they can synchronize all their lights to do the same thing.